‘Nothing can stop me,” sings Dawn Richard on the title track of New Breed, “I do what I wanna.” Of course, pop stars are always saying things like that, but Richard is more headstrong and unique than most.

The path from TV talent show pop star to edgy leftfield auteur is largely untrodden – or at least it was until Richard started gamely tramping down it. She first came to prominence in the US as a member of Danity Kane, a girl group manufactured to Sean Combs’s specifications on the MTV series Making the Band. After their brief career ended in the obligatory acrimonious split (an attempted reunion in 2013 was drawn to a swift conclusion by a fight), and following an equally brief period in Combs’s ho-hum collective Diddy-Dirty Money, Richard took off on a solo career no one could have predicted. She made three critically hosannaed, interlinked concept albums. Lyrical imagery drawn from science-fiction and medieval warfare crashed into futuristic production and songs that frequently dispensed with standard verse-chorus-verse structures in favour of a stream-of-consciousness approach.

Behind its extraordinary cover – Richard reclining on the front porch of a derelict wooden house, clad in silver platform boots and a vast white feathered headdress of the Washitaw, a group of black Americans who claim to be a sovereign Native American nation – New Breed is a slightly more straightforward prospect than its predecessors. It is rooted in her home town of New Orleans: the lyrics are thick with references to locations in the city, and there are samples of discussions of local cultural traditions and of artists shouting out to their home town from the stage between songs. But New Orleans’ musical imprint is subtle. If the ghosts of the R&B records that poured out of the city in the late 50s and early 60s haunt the sampled voices on opener The Nine, you would never characterise the results as an obvious homage.

Similarly, there’s a hint of the Meters’ taut funk about the guitar line of Dreams and Converse, and an echo of Allen Toussaint in the lovely, rolling piano of We, Diamonds, but they sit amid thoroughly modern pop songs. The former is a wash of dreamy synthesiser and house-influenced beats, the latter boasts a mesh of overlapping voices and the kind of chorus that – in a fairer world, where Richard’s placings on end-of-year-lists were matched on the actual charts – could provoke arenas to sing along. Meanwhile, two of the album’s best tracks are built around music that, geographically speaking, couldn’t be further from Louisiana: Spaces features a gorgeous, rippling synthesiser motif that sounds as if it stepped off a mid-70s Tangerine Dream album, while Jealousy maps out an intriguing space between dubby lover’s rock and DJ Screw.

Listening to tracks like that, one wonders if the weirdness of Richard’s work might have been overstated. There is a tendency in some quarters to write about her music in a way that makes it sound avant garde and challenging, as if you have to steel yourself to listen to it. It does her a disservice. The music on New Breed is often hugely inventive but it also functions as pop: you get the feeling she spends as much time bulletproofing her choruses as she does tinkering with the futuristic sound design. The fact that her music exists on the margins (tellingly, the abortive Danity Kane reunion came about after Richard failed to generate enough money on Kickstarter to make her 2015 album Blackheart) seems to say more about how narrow the confines of mainstream pop currently are, than about any lack of commerciality on her part.

This fact clearly hasn’t escaped Richard. As well as lyrics about sexuality, or warning a partner’s ex off in no uncertain terms (“I know you feel you have a right to call him – you don’t”), she keeps returning to the subject of how hard she has had to work to forge her musical identity. The spoken-word introductions to Spaces and We, Diamonds offer a list of compelling reasons for why the pop landscape isn’t more densely populated with figures like her, railing against the way the music industry categorises black women and doubts their ability to be anything more than divas. You can see why she feels she must reiterate that doing what she does involves real struggle, and not just because it highlights a more general injustice.

Adventurous but never abstruse, New Breed sounds effortless, as though transforming yourself from a manufactured pop star into a unique artist is the easiest thing in the world: “This shit is simple, do the math, I’m the answer and the proof,” she sings on the title track. But of course it isn’t: making it seem so is just one of its author’s multitude of talents.